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Q.
The ratio of densities of nitrogen and oxygen is 14:16. The temperature at which the speed of sound in nitrogen will be same as that of oxygen at $ 55{}^\circ C $ is
EAMCETEAMCET 1999
Solution:
The velocity in a gas is given $ c=\sqrt{\frac{3RT}{{{V}_{\rho }}}} $ given $ {{\rho }_{{{N}_{2}}}}:{{\rho }_{{{O}_{2}}}}=14:16 $ Hence, $ c\propto \sqrt{\frac{T}{\rho }} $ Since, velocity in nitrogen and oxygen is same $ \sqrt{\frac{{{T}_{{{N}_{2}}}}}{{{\rho }_{{{N}_{2}}}}}}=\sqrt{\frac{{{T}_{{{O}_{2}}}}}{{{\rho }_{{{O}_{2}}}}}} $ or $ {{T}_{{{N}_{2}}}}{{\rho }_{{{O}_{2}}}}={{T}_{{{O}_{2}}}}{{\rho }_{{{N}_{2}}}} $ $ {{T}_{{{N}_{2}}}}=\frac{{{\rho }_{{{N}_{2}}}}}{{{\rho }_{{{O}_{2}}}}}\times {{T}_{{{O}_{2}}}}=\frac{14}{16}\times 55=48.125 $ $ \approx 48{{\,}^{o}}C $